Answer to Question #42518 in Algebra for shasha

Question

A projectile is thrown upward so that its distance above the ground after t seconds is h = -16t2 + 672t. After how many seconds does it reach its maximum height?

21 s

31.5 s

42 s

10 s

help me please and show work

Answer 1

The equation of parabola h=at²+bt+c is in a standard form. The vertex of parabola is either the maximum or minimum value of parabola. In this problem a=-16<0, that is why we deal with the maximum value of parabola.The t-coordinate of the vertex can be found by the formula t₀= -b/(2a)=-672/(2*(-16))=21 (s).
Answer: the projectile reach its maximum height after 21 s.